Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}4x+6y &= 5 \\ -8x-6y &= -1\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-4x = 4$ Divide both sides by $-4$ and reduce as necessary. $x = -1$ Substitute $-1$ for $x$ in the top equation. $4( -1)+6y = 5$ $-4+6y = 5$ $6y = 9$ $y = \dfrac{3}{2}$ The solution is $\enspace x = -1, \enspace y = \dfrac{3}{2}$.